Full Practice Exam 30 — Module 2

Questions in this quiz (22)

1. The quadratic function $$g$$ is defined by $$g(x)=kx^2+11$$ for some constant $$k$$. If $$g(-7)=6$$, what is the value of $$g(7)$$?

   • $$-6$$
   • $$5$$
   • $$6$$
   • $$17$$

2. $$|a-3|+1=n$$If $$n=3$$, which value of $$a$$ satisfies the equation above?

   • $$-5$$
   • $$-1$$
   • $$1$$
   • There is no such value of $$a$$.

3. Let $$cp=-6$$. Given that $$\frac{z-1}{3}=cp,$$ what is the value of $$z$$?

   • $$-19$$
   • $$-18$$
   • $$-17$$
   • $$-2$$

4. $$g(x)=bx^2-21$$The quadratic function $$g$$ is defined below. If $$b$$ is a constant and $$g(-6)=3$$, what is the value of $$g(6)$$?

   • $$-24$$
   • $$-18$$
   • $$-3$$
   • $$3$$

5. A sporting goods company is attempting to find the optimum selling price of one of its products. The product presently has an average selling price of $$\$91$$, at which an average of $$2000$$ are sold per month. It is expected that the average number sold per month will decrease by $$200$$ for each $$\$1$$ increase in the selling price. Which equation models the average amount $$A$$, in dollars per month, earned in sales for this product based on an $$\$x$$ increase in the selling price?

   • $$A=(91+x)(2000-200x)$$
   • $$A=(91+x)(2000+200x)$$
   • $$A=x(2000-200x)$$
   • $$A=2000(91+x)-200x$$

6. The graph of a polynomial function $$p(x)$$ is a parabola. If $$p(x)$$ has zeros at $$x=16$$ and $$x=14$$, which of the following is the $$x$$-coordinate of the vertex of the parabola?

   • $$-1$$
   • $$0$$
   • $$1$$
   • $$15$$

7. A rectangular rug is $$12$$ feet wide and is to be located exactly in the middle of a floor. The floor is $$20$$ feet wide. Which equation can be used to find both values of $$x$$ if $$x$$ is the distance, in feet, from the left edge of the floor to each edge of the rectangular rug?

   • $$|x-12|=10$$
   • $$|x-10|=12$$
   • $$2|x-12|=10$$
   • $$2|x-10|=12$$

8. When $$x\neq-3$$, which of the following gives the result of dividing $$4x+3$$ by $$x+3$$?

   • $$\frac{4+3}{3}$$
   • $$4+1$$
   • $$4-\frac{9}{x+3}$$
   • $$4-\frac{9}{4x+3}$$

9. A school club ordered a shirt for each of its members. The color and size distribution of the shirts is shown in the table below.If one shirt is randomly selected, what is the probability that it is medium and red or large and blue?

   • $$\frac{13}{74}$$
   • $$\frac{13}{37}$$
   • $$\frac{24}{37}$$
   • $$\frac13+\frac4{11}$$

10. Eric creates and sells rings and bracelets. He makes a profit of $$\$9.20$$ for each ring and $$\$12.40$$ for each bracelet. Let $$x$$ represent the number of rings he sells and $$y$$ represent the number of bracelets he sells. Eric's goal this month is to sell at least $$95$$ rings and bracelets and to make a total profit of at least $$\$1,650$$. Which system of inequalities can be used to represent his goal for this month?

    • $$9.20x+12.40y\ge1650$$$$x+y\ge95$$
    • $$9.20x+12.40y\ge95$$$$x+y\ge1650$$
    • $$\frac{x}{9.20}+\frac{y}{12.40}\ge1650$$$$x+y\ge95$$
    • $$\frac{x}{9.20}+\frac{y}{12.40}\ge95$$$$x+y\ge1650$$

11. $$8x-y=27$$$$-x^2-3x+y=-21$$Which of the following gives all solutions to the system?

    • $$(-3,-2)$$
    • $$(2,3)$$
    • $$(-3,-21)$$ and $$(-2,-23)$$
    • $$(2,-11)$$ and $$(3,-3)$$

12. A local internet provider charges Stephanie a fixed amount each month in addition to the start-up fees that were paid at the beginning of the service period. The equation $$d=109+16m$$ represents the total amount $$d$$, in dollars, that she has paid for this internet service after $$m$$ monthly payments. According to the equation, how much did Stephanie pay in start-up fees?

    • 109

13. $$\frac{t}{(y+10)^2-12(y+10)+36}$$Given that the expression below is undefined, what is the value of $$y$$?

    • -4

14. Find the perimeter, in feet, of triangle $$UVW$$ given the following information:1. Triangle $$PQR$$ is similar to $$UVW$$.2. Triangle $$PQR$$ has side lengths $$9,9,$$ and $$7$$ feet.3. The shortest side of triangle $$UVW$$ measures $$21$$ feet.

    • $$\frac{25}{3}$$
    • $$27$$
    • $$48$$
    • $$75$$

15. A circle in the $$xy$$-plane has center $$(-9,-15)$$ and a radius with endpoint $$\left(-\frac{33}{5},-14\right)$$. What is the equation of the circle?

    • $$(x-9)^2+(y-15)^2=\frac{13}{5}$$
    • $$(x-9)^2+(y-15)^2=\frac{169}{25}$$
    • $$(x+9)^2+(y+15)^2=\frac{13}{5}$$
    • $$(x+9)^2+(y+15)^2=\frac{169}{25}$$

16. Robert sampled the scat of $$186$$ black bears and found that $$58$$ of them contained traces of fish. According to the data collected, what is the ratio of scat that contained traces of fish to scat that did not contain traces of fish?

    • $$64:29$$
    • $$29:93$$
    • $$29:64$$
    • $$64:93$$

17. A plastic part is composed of a right circular cylinder and two right circular cones. The cylinder has height $$21$$ cm, each cone has height $$11$$ cm, and the radius is $$9$$ cm. Approximately what volume of plastic, in cubic centimeters, is needed to make each part?

    • $$1,866.11$$
    • $$5,343.85$$
    • $$6,276.90$$
    • $$7,209.96$$

18. The inequality $$9+9x$$ > $$12+8x$$ is true for all of the following values of $$x$$ except which one?

    • $$-1$$
    • $$4$$
    • $$5$$
    • $$9$$

19. The figure shows a regular hexagon with sides of length $$a$$ and a square with sides of length $$a$$. If the area of the hexagon is $$384\sqrt3$$ square inches, what is the area, in square inches, of the square?

    • 256

20. Theresa ran on a treadmill for thirty minutes, and her time and speed are shown in the graph. According to the graph, which of the following statements is NOT true concerning Theresa's run?

    • Theresa ran at a constant speed for five minutes.
    • Theresa's speed was increasing for a longer period of time than it was decreasing.
    • Theresa's speed decreased at a constant rate during the last five minutes.
    • Theresa's speed reached its maximum during the last ten minutes.

21. The table shows the percent of residents who earned a bachelor's degree or higher in $$7$$ states.The median percent for all $$50$$ states was $$26.95\%$$. What is the difference between the median percent for these $$7$$ states and the median for all $$50$$ states?

    • $$0.05\%$$
    • $$0.95\%$$
    • $$1.22\%$$
    • $$7.45\%$$

22. The scatterplot shows the densities of $$7$$ planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown. According to the scatterplot, which of the following statements is true about the relationship between a planetoid's average distance from the Sun and its density?

    • Planetoids that are more distant from the Sun tend to have lesser densities.
    • Planetoids that are more distant from the Sun tend to have greater densities.
    • The density of a planetoid that is twice as far from the Sun as another planetoid is half the density of that other planetoid.
    • The distance from a planetoid to the Sun is unrelated to its density.